A police officer stands next to the body of a man (covered by a white sheet) who was shot and killed by an off-duty police officer Monday on Atlantic Avenue in Brooklyn, near Bradford Street, following a traffic dispute.Robert Mecea

An off-duty cop shot and killed a 37-year-old man early Monday after a road-rage incident in Brooklyn, law enforcement sources told The Post.

The cop, a three-year veteran assigned to the 79th Precinct in Bedford-Stuyvesant, was driving at about 12:15 a.m. when he got into a beef with the other motorist, Delron “Smalls” Dempsey, in Cypress Hills, the sources said.

Both men pulled over in front of 2736 Atlantic Ave. and Dempsey got out of his silver Kia, approached the cop’s car and starting punching him through an open window as the officer remained seated, the sources said.

After he was struck in the face and head numerous times, the cop, fearing for his life, pulled out his weapon and fired three times, striking Dempsey at least once in the chest, sources added.

Dempsey died at the scene.

The unidentified cop, who was not in uniform, was taken to Jamaica Hospital, where he was treated for multiple facial injuries, the sources said.

Dempsey, a Jersey City resident, was on his way to a fireworks display with his wife and two kids when the deadly incident occurred, his brother told reporters shortly after the shooting.

“His wife was in the car with him, his two kids was with him,” Victor Dempsey told CBS 2. “They were going to see fireworks up by whatever park is in the neighborhood.”

“It has to stop. It’s not right that [cops] get a gun and a badge and they can do what they want to do.”

Dempsey’s relatives, who were at the scene, claimed he had been shot in the head.

“He’s dead. Lying here, no ambulance, no nothing,” said a cousin, refusing to be named.

“They shot him in the head.”

A Long Island woman who identified herself as the dead man’s mother-in-law said he was a cab driver but declined to comment further.

Police had the area marked off with crime-scene tape and were still investigating the incident.